Question

5. A sales manager used linear regression to find the positive linear relationship between advertising expenditures and sales. the equation was calculated from the following data from 7 randomly selected advertising campaigns:

Advertising Expenditures - $8,000 / $22,000 / $15,000 / $39,000 / $32,000 / $12,000 / $45,000

Sales - $95,000 / $190,000 / $125,000 / $ 225,000 / $285,000 / $150,000 / $350,000

If the sales manager used regression equation to predict the amount of sales that he can expect for advertising expenditures of $35,000, and then used the equation to predict the amount of sales he can expect for advertising expenditures of $65,000, Which prediction would probably be more reliable and why?

Answer 1

The prediction of the sales based on the advertising expenditures of $35,000 is more reliable because the value of advertising expenditure of $35,000 is lies within the range for the values for advertising expenditures, but the value for advertising expenditures of $65,000 is not lies within the range of values for advertising expenditures. The range for advertising expenditures is given as $8,000 to $45,000. If we use regression equation for the prediction of sales based on the value out of given range, then there would be case of extrapolation and this estimate would be less reliable.